Factorization of string amplitudes is one way of constructing string i
nteraction vertices. We show that correlation functions in string theo
ry can be conveniently factorized using loop variables representing de
lta functionals. We illustrate this construction with some examples wh
ere one particle is off-shell. These vertices are ''correct'' in the s
ense that they are guaranteed, by construction, to reproduce S-matrix
elements when combined with propagators in a well-defined way.